The SecureSCM project (www.securescm.org) aims to develop cryptographic solutions to the problem of data sharing in Supply Chain Optimization (SCO). The SCO problem has a precise mathematical structure. It is an instance of the general Linear Programming (LP) problem. However, standard techniques for LP problems are not suitable for this purpose because they require participants to reveal priva...

Correlation clustering is an exciting area of research in the fields of graphical models and image segmentation. In this article we study the linear programming (LP) relaxation corresponding to PlanarCC and the multi-cut LP relaxation which are two methods for correlation clustering. We demonstrate that they have equal value when optimized. This provides justification for the use of PlanarCC wh...

Recently, Linear Programming (LP)-based relaxations have been shown promising in boosting the performance of exact MAX-SAT solvers. We compare Semidefinite Programming (SDP) based relaxations with LP relaxations for MAX2SAT. We will show how SDP relaxations are surprisingly powerful, providing much tighter bounds than LP relaxations, across different constrainedness regions. SDP relaxations can...

In this note we show that Ye-Todd-Mizuno's O(p nL)-iteration homogeneous and self-dual linear programming (LP) algorithm possesses quadratic convergence of the duality gap to zero. In the case of infeasibility, this result shows that a homogenizing variable quadratically converges to zero and implies that the iterates of the (original) LP variable quadratically diverge. Thus, we have establishe...

This paper describes a neural network based controller for allocating capacity in a telecommunications network. This system was proposed in order to overcome a "real time" response constraint. Two basic architectures are evaluated: 1) a feedforward network-heuristic and; 2) a feedforward network-recurrent network. These architectures are compared against a linear programming (LP) optimiser as a...

Linear programming (LP) is one of the great successes to emerge from operations research and management science. It is well developed and widely used. LP problems in practice are often based on numerical data that represent rough approximations of quantities that are inherently difficult to estimate. Because of this, most LP-based studies include a postoptimality investigation of how a change i...

FOLPI is a Linear Programming-based planning system that can be used by forest managers without a detailed knowledge of Linear Programming (LP). It is compatible with IFS, an interactive forest simulator widely used by the New Zealand Forest Service. The system allows the user to state the problem in forestry terms, within a framework similar to that used by IFS. The problem statement is automa...

We consider a system of nonlinear ordinary differential equations for the solution of linear programming (LP) problems that was first proposed in the mathematical biology literature as a model for the foraging behavior of acellular slime mold Physarum polycephalum, and more recently considered as a method to solve LPs. We study the convergence time of the continuous Physarum dynamics in the con...

In recent years we have seen an increasing interest in combining constraint satisfaction problem (CSP) formulations and linear programming (LP) based techniques for solving hard computational problems. While considerable progress has been made in the integration of these techniques for solving problems that exhibit a mixture of linear and combinatorial constraints, it has been surprisingly diff...

A disadvantage of the SDP (semidefinite programming) relaxation method for quadratic and/or combinatorial optimization problems lies in its expensive computational cost. This paper proposes a SOCP (second-order-cone programming) relaxation method, which strengthens the lift-and-project LP (linear programming) relaxation method by adding convex quadratic valid inequalities for the positive semid...